CN108846186B - Brittle material discrete element modeling method considering hole defect shape and distribution randomness thereof - Google Patents
Brittle material discrete element modeling method considering hole defect shape and distribution randomness thereof Download PDFInfo
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Abstract
The invention discloses a brittle material discrete element modeling method considering hole defect shapes and distribution randomness thereof, which is mainly used for discrete element simulation research of brittle materials such as engineering ceramics and the like. Firstly, establishing a closed area, and adding a certain amount of particles with the radius which is subject to uniform or normal distribution into the closed area to ensure that the particles are tightly arranged; then, selecting a proper contact model to endow the particles with a connecting bond with certain strength; secondly, determining a certain number of hole defect centers with random positions through a position random function, and constructing each hole defect polygon with shape randomness; and finally, deleting the wall of the closed area, and deleting the particles in the polygon to form the hole defect. The method is easy to realize programming and simple and convenient to debug, and more accords with the existing state of the actual defect of the brittle material, so that the simulation experiment result is more accurate, the actual situation is more accorded, and the effectiveness of the simulation experiment is improved.
Description
Technical Field
The invention belongs to research on simulation processes of discrete element modeling experiments of brittle materials such as engineering ceramics and the like, and particularly relates to a brittle material discrete element modeling method considering hole defect shapes and distribution randomness thereof.
Background
Because of the rapid development of computer technology, the way of simulating various materials by computer modeling to perform simulation experiments is supported and accepted more and more, and compared with actual experiments, the computer modeling simulation has the capability of testing and measuring various parameters, the values of the parameters are approximate to real values, the parameter debugging is convenient and fast, the cost is low, and valuable experiment parameters and result comparison can be provided for further real experiments.
At present, the model simulation of random shapes by adopting discrete elements is mostly found in the research of rocks and earth and stones, and a new brittle material discrete element modeling method suitable for simulating the shape and randomly distributing the hole-containing defects is needed to be provided. From the known literature and patents, no modeling method has been reported which can be applied to brittle material simulation by using discrete element method to generate hole defects with random shapes and positions.
Disclosure of Invention
In order to achieve the purpose, the brittle material discrete element modeling method considering the shape of the hole defects and the distribution randomness of the hole defects is provided.
The technical scheme adopted by the invention is a brittle material discrete element modeling method considering the shape and distribution randomness of hole defects, which is characterized in that the method for establishing a discrete element model comprises the following steps:
1) enclosing a closed calculation area by establishing a boundary wall;
2) generating particles in a closed calculation area, wherein the radius of the particles is subjected to uniform distribution or normal distribution and the particles are randomly generated in position, assigning the density, the damping and the rigidity of the particles and the properties of an inter-particle contact model, and enabling the particles to reach a stable and compact arrangement state through the interaction of the particles to obtain a base material model;
3) generating a polygon representing the hole defect with random position and random shape; determining a certain number of hole defect centers with random positions in the calculation area through a position random function; to control the size of the polygon representing the hole defect, the polygon is generated between two concentric circles, the inner circle being denoted CiAnd the outer circle is denoted as Ci+1The centers of the two concentric circles are the center of the hole defect; the number of the polygon edges is controlled by randomly generated node numbers, and the shape of the polygon is controlled by the distance from each node to the center of the polygon and the central angle corresponding to each edge of the polygon;
4) circularly generating a plurality of polygons K representing hole defects with random positions and random shapes in the calculation area according to the steps 1), 2) and 3)1、K2....Kn；
5) Grouping the particles with the center of the particles located in all the generated polygons K1、K2....KnWithin, defined as group I, the particle center is located in all the generated polygons K1、K2....KnOtherwise, defining the group as group II;
6) and deleting the boundary wall, and deleting the particles in the group I to obtain the brittle material discrete element model containing the hole defects with random shapes and distribution.
According to the brittle material discrete element modeling method considering the shape and the distribution randomness of the hole defects, the size and the shape of the closed calculation area in the step 1) can be changed;
according to the brittle material discrete element modeling method considering the shape of the hole defect and the distribution randomness of the hole defect, the density, the damping and the rigidity of the particles in the step 2) and the properties of the inter-particle contact model can be adjusted, wherein the contact model is a connecting key model, and the types of inter-particle key connection are parallel keys and contact keys;
in the brittle material discrete element modeling method considering the shape and the distribution randomness of the hole defects, the hole defects with random positions and random shapes in the step 3) are irregular polygons, a certain number of hole defect centers are determined through a random function in a calculation area and are used as the center points of the polygons representing the hole defects, the centers are used as the centers of two concentric circles, and the polygons are generated between the two concentric circles;
in the above brittle material discrete element modeling method considering the shape of the hole defect and the distribution randomness thereof, the generation sequence of the two circles in the defect generation program in step 3) is as follows: firstly, an initial radius r is determined according to the average radius of the required target defect0Then the initial radius r is set0And the radius change amount deltarRespectively summing and differencing to obtain a circle Ci+1Radius r ofi+1Circle CiRadius r ofiThe polygon representing the hole defect is on a circle Ci+1Circle CiGenerating in the annular region of the composition; of polygonal shapeThe generation sequence is as follows: firstly, randomly generating a node in an area formed by two concentric circles, and then sequentially generating other nodes according to the node and the coordinates of the circle center, wherein the nodes are sequentially connected to form a closed polygon;
in the above brittle material discrete element modeling method considering the shape and distribution randomness of the hole defects, the shape randomness of the polygon representing the hole defects, the positions of which are randomly distributed and the shape of which is random, in the step 3) can be controlled by adjusting a theta increment factor in a formula (8), the theta increment is increased, and the generated central angle is larger, so that the defect shape approaches from a regular polygon to a flat and long and narrow shape;
in the modeling method for discrete elements of brittle materials considering the shape and the distribution randomness of the hole defects, the deletion of the particles in the group I in the step 6) is realized based on the way of grouping the particles.
Drawings
FIG. 1 is a flow chart of a brittle material discrete element modeling method considering the shape of hole defects and their distribution randomness.
Fig. 2 is a diagram of an established square closed region model.
FIG. 3 is a diagram of the established basis model of discrete meta-particles.
FIG. 4 is a diagram of a model of a random polygonal hole defect.
FIG. 5 is a diagram of a model of random polygonal hole defects formed by increasing the incremental factor θ.
FIG. 6 is a diagram of a sample model for random generation and random distribution of created hole defect polygons.
FIG. 7 is a graph taken at θMAnd (2) randomly generating a polygonal hole defect and randomly distributing the polygonal hole defect to obtain a sample model diagram.
FIG. 8 is a diagram of a discrete element model of a brittle material established taking into account the shape of hole defects and their randomness in distribution.
FIG. 9 is a graph of the established value θMAnd 2, considering the shape of the hole defect and the distribution randomness thereof.
Detailed Description
The invention will be further explained with reference to the drawings.
A brittle material discrete element modeling method considering the shape and distribution randomness of hole defects is characterized in that the step of establishing a discrete element model of the hole defects is as follows:
1) enclosing a closed calculation area by establishing a boundary wall;
2) generating particles in a closed calculation area, wherein the radius of the particles is subjected to uniform distribution or normal distribution and the particles are randomly generated in position, assigning the density, the damping and the rigidity of the particles and the properties of an inter-particle contact model, and enabling the particles to reach a stable and compact arrangement state through the interaction of the particles to obtain a base material model;
3) generating a polygon representing the hole defect with random position and random shape; determining a certain number of hole defect centers with random positions in the calculation area through a position random function; to control the size of the polygon representing the hole defect, the polygon is generated between two concentric circles, the inner circle being denoted CiAnd the outer circle is denoted as Ci+1The centers of the two concentric circles are the centers of the hole defects; the number of the polygon edges is controlled by randomly generated node numbers, and the shape of the polygon is controlled by the distance from each node to the center of the polygon and the central angle corresponding to each edge of the polygon;
4) circularly generating a plurality of polygons K representing hole defects with random positions and random shapes in the calculation area according to the steps 1), 2) and 3)1、K2....Kn；
5) Grouping the particles with the center of the particles located in all the generated polygons K1、K2....KnWithin, defined as group I, the particle center is located in all the generated polygons K1、K2....KnOtherwise, defining the group as group II;
6) and deleting the boundary wall, and deleting the particles in the group I to obtain the brittle material discrete element model containing the hole defects with random shapes and distribution.
The specific process is as follows:
1) establishing a closed calculation area surrounded by the boundary walls through programming, wherein a square calculation area is taken as an example, the center of the square calculation area is located at the coordinate origin (0, 0), and the side length is L, as shown in FIG. 2;
2) generating particles in a closed calculation region, as shown in fig. 3, wherein the particle radius follows uniform distribution or normal distribution and the positions are randomly generated, assigning the density, damping and rigidity properties of the particles and the properties of the contact model among the particles, and enabling the particles to reach a stable and compact arrangement state through the interaction of the particles to obtain a base material model;
3) generating a polygon characterizing the hole defect with a random position and a random shape, as shown in fig. 4, wherein the generation process is as follows:
(1) determining a certain number of hole defect centers with random positions through a position random function in a calculation area, taking the hole defect centers as the center points of polygons representing hole defects, taking the points as the centers of two concentric circles, generating the polygons between the two concentric circles, taking a square area as an example, and generating coordinate points (a) of the hole defect centersi,bi) Satisfies the following conditions:
(2) The radius of two concentric circles is defined, and an initial radius r is determined according to the average radius of the target defect0Then the initial radius r is set0And the radius change amount deltarRespectively summing and differencing to obtain a circle Ci+1Radius r ofi+1Circle CiRadius r ofiThe polygon representing the hole defect is on a circle Ci+1Circle CiThe size of the area is randomly changed, and the change amplitude is formed by radius change quantity deltarControl, ΔrRadius increment q from the initial definitionrAnd a random number mrIn relation, the calculation formula is as follows:
Δr＝qr·mr (2)
ri＝r0-0.5Δr (3)
ri+1＝r0+0.5Δr (4)
in the formula, mrIs (0-1) random numbers uniformly distributed in the oral administration;
(3) defining nodes of the polygon, controlling the number of edges of the polygon by the number n of randomly changing nodes, controlling the shape of the polygon by the distance from each node to the center of the polygon and the central angle corresponding to each edge of the polygon, if the shape is on the circle Ci+1And the circle CiRandomly generates a node p in the ring region betweeniThen p isiCoordinates of the points:
xpi＝xi+ρicos(θi) (5)
ypi＝yi+ρisin(θi) (6)
in the formula, the center o of the concentric circleiDistance to node piComprises the following steps:
ρi＝ri+Δr (7)
the average value of the included angles between the line segments from each node of the polygon to the center point thereof and the horizontal coordinate axis is
The first node is denoted as p1The ith node is denoted as piThe nodes are generated in the counterclockwise direction; p is a radical of1To the center o of a circleiIs denoted as line segment p1oi，piTo the center o of a circleiIs denoted as line segment pioiLine segment p1oiThe included angle between the X axis of the rectangular coordinate system is recorded as theta1Line segment pioiThe included angle between the X axis of the rectangular coordinate system is recorded as thetaiThe direction of the included angle is positive in the counterclockwise direction; m isθIs a random number (theta) uniformly distributed in the form of (1-1)MIs theta increment factor, the initial value is 0, then thetaiComprises the following steps:
the total number of nodes n of the polygon is:
n＝[n0+qn·mn] (9)
in the formula, n0The number of polygon average nodes; q. q.snFor the initially defined increment of the number of nodes, mnThe random number is (1-1) uniformly distributed in the internal application;
next generated node pjThe coordinates of (a) are:
xpj＝xj+ρjcos(θj) (10)
ypj＝yj+ρjsin(θj) (11)
n-th node pnHas the coordinates of
xpn＝xn+ρncos(θn) (12)
ypn＝yn+ρnsin(θn) (13)
(4) The n nodes are connected in sequence to form a closed polygon with random shape and position;
the shape randomness of the polygons representing the hole defects, which are randomly distributed and have random shapes, can be controlled by adjusting a theta increment factor in a formula (8), wherein the theta increment is increased, and the generated central angle is larger, so that the defect shapes can be approached from regular polygons to flat and long and narrow shapes, as shown in fig. 5;
4) circularly generating a plurality of polygons K representing the hole defects with random positions and random shapes in the calculation area according to the steps1、K2....KnFIG. 7 is a view taken on θ, as shown in FIG. 6MAnd (2) randomly generating a polygonal hole defect and randomly distributing the polygonal hole defect to obtain a sample model diagram.
5) The particles in the square discrete element particle model are divided into two groups, all the particles in the defect shape, namely the particles with the midpoint coordinate within the defect, are set as the I group, and the particles outside the defect shape, namely the particles with the midpoint coordinate outside the defect, are set as the I groupSetting granules as group II; then deleting the particles in the group I to obtain a discrete element model containing random shape and random position defects, as shown in FIG. 8, and taking theta for establishing the model in FIG. 9MAnd 2, considering the shape of the hole defect and the distribution randomness thereof.
Claims (6)
1. A brittle material discrete element modeling method considering hole defect shapes and distribution randomness thereof is characterized by comprising the following modeling steps:
1) enclosing a closed calculation area by establishing a boundary wall;
2) generating particles in a closed calculation area, wherein the radius of the particles is subjected to uniform distribution or normal distribution and the particles are randomly generated in position, assigning the density, the damping and the rigidity of the particles and the properties of an inter-particle contact model, and enabling the particles to reach a stable and compact arrangement state through the interaction of the particles to obtain a base material model;
3) generating a polygon representing the hole defect with random position and random shape; determining a certain number of hole defect centers with random positions in the calculation area through a position random function; to control the size of the polygon representing the hole defect, the polygon is generated between two concentric circles, the inner circle being denoted CiAnd the outer circle is denoted as Ci+1The centers of the two concentric circles are the centers of the hole defects; the number of the polygon edges is controlled by randomly generated node numbers, and the shape of the polygon is controlled by the distance from each node to the center of the polygon and the central angle corresponding to each edge of the polygon;
4) circularly generating a plurality of polygons K representing hole defects with random positions and random shapes in the calculation area according to the steps 1), 2) and 3)1、K2....Kn；
5) Grouping the particles with the center of the particles located in all the generated polygons K1、K2....KnWithin, defined as group I, the particle center is located in all the generated polygons K1、K2....KnOtherwise, defining the group as group II;
6) and deleting the boundary wall, and deleting the particles in the group I to obtain the brittle material discrete element model containing the hole defects with random shapes and distribution.
2. The modeling method for discrete elements of brittle material with hole defect shape and its distribution randomness considered as claimed in claim 1, wherein the closed calculation region in step 1) can be designed into any shape theoretically, and the size and shape of the calculation region can be adjusted, where a square region is taken as an example, the midpoint is located at (0, 0), and the side length is L.
3. The method according to claim 1, wherein the density, damping, stiffness properties and inter-particle contact model properties of the particles in step 2) are adjustable, wherein the contact model is a connection bond model, and the inter-particle bond connection type is a parallel bond or a contact bond.
4. The modeling method for discrete elements of brittle material with hole defects in consideration of their shapes and their distribution randomness as claimed in claim 1, wherein the polygon representing hole defects with randomly distributed positions and random shapes in step 3) is generated as follows:
(1) determining a certain number of hole defect centers with random positions through a position random function in a calculation area, taking the hole defect centers as the center points of polygons representing hole defects, taking the points as the centers of two concentric circles, generating the polygons between the two concentric circles, taking a square area as an example, and generating coordinate points (a) of the hole defect centersi,bi) Satisfies the following conditions:
(2) the radius of two concentric circles is defined, and an initial radius r is determined according to the average radius of the target defect0Then will beInitial radius r0And the radius change amount deltarRespectively summing and differencing to obtain a circle Ci+1Radius r ofi+1Circle CiRadius r ofiThe polygon representing the hole defect is on a circle Ci+1Circle CiThe size of the area is randomly changed, and the change amplitude is formed by radius change quantity deltarControl, ΔrRadius increment q from the initial definitionrAnd a random number mrIn relation, the calculation formula is as follows:
△r＝qr·mr (2)
ri＝r0-0.5△r (3)
ri+1＝r0+0.5△r (4)
in the formula, mrIs (0-1) random numbers uniformly distributed in the oral administration;
(3) defining nodes of the polygon, controlling the number of edges of the polygon by the number n of randomly changing nodes, controlling the shape of the polygon by the distance from each node to the center of the polygon and the central angle corresponding to each edge of the polygon, if the shape is on the circle Ci+1And the circle CiRandomly generates a node p in the ring region betweeniThen p isiCoordinates of the points:
xpi＝xi+ρicos(θi) (5)
ypi＝yi+ρisin(θi) (6)
in the formula, the center o of the concentric circleiDistance to node piComprises the following steps:
ρi＝ri+△r (7)
the average value of the included angles between the line segments from each node of the polygon to the center point thereof and the horizontal coordinate axis is
The first node is denoted as p1The ith node is denoted as piThe nodes are generated in the counterclockwise direction; p is a radical of1To the center o of a circleiIs denoted as line segment p1oi，piTo the center o of a circleiIs denoted as line segment pioiLine segment p1oiThe included angle between the X axis of the rectangular coordinate system is recorded as theta1Line segment pioiThe included angle between the X axis of the rectangular coordinate system is recorded as thetaiThe direction of the included angle is positive in the counterclockwise direction; m isθIs a random number (theta) uniformly distributed in the form of (1-1)MIs theta increment factor, the initial value is 0, then thetaiComprises the following steps:
the total number of nodes n of the polygon is:
n＝[n0+qn·mn] (9)
in the formula, n0The number of polygon average nodes; q. q.snFor the initially defined increment of the number of nodes, mnThe random number is (1-1) uniformly distributed in the internal application;
next generated node pjThe coordinates of (a) are:
xpj＝xj+ρjcos(θj) (10)
ypj＝yj+ρjsin(θj) (11)
n-th node pnHas the coordinates of
xpn＝xn+ρncos(θn) (12)
ypn＝yn+ρnsin(θn) (13)
(4) The n nodes are connected in sequence to form a closed polygon with random shape and position.
5. The modeling method of discrete elements of brittle material with hole defect shape and distribution randomness taken into account as claimed in claim 1, wherein the shape randomness of the polygon representing hole defects with randomly distributed positions and random shapes in step 3) can be controlled by adjusting the theta increment factor in formula (8), the theta increment is increased, and the generated central angle is larger, so that the defect shape approaches from regular polygon to flat and long and narrow, the defect shape becomes more diversified, and different shape requirements are met.
6. The modeling method of discrete elements of brittle material with hole defect shape and its distribution randomness taken into account of claim 1, characterized in that the elimination of particles in group I in step 6) is implemented based on grouping particles, so that the particles in the discrete element particle model are divided into two groups, all particles in the polygon of hole defect, i.e. the particles with midpoint coordinate within the defect, are set as group I, and particles outside the polygon of hole defect, i.e. the particles with midpoint coordinate outside the defect, are set as group II; and then deleting the I group by using a deleting grouping mode to obtain the discrete meta-model containing the random shape and random position defects.
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| CN109978995B (en) * | 2019-03-28 | 2023-04-07 | 湘潭大学 | Method for generating brittle material containing random irregular polyhedron hole defects |
| CN110083936B (en) * | 2019-04-26 | 2023-06-16 | 中煤科工集团重庆研究院有限公司 | Method for generating crushable crushed stone particles by considering shape parameters |
| CN110688748A (en) * | 2019-09-19 | 2020-01-14 | 湘潭大学 | Single-particle discrete element numerical sample modeling method with random shape |
| CN110879926B (en) * | 2019-12-16 | 2023-05-23 | 湘潭大学 | Method for cutting heat simulation calculation in brittle material cutting process |
| CN112632780B (en) * | 2020-12-24 | 2023-02-03 | 西北工业大学 | Method for establishing three-dimensional model of composite material |
| CN113868734B (en) * | 2021-09-08 | 2024-04-19 | 中铁二十局集团第六工程有限公司 | Distribution characteristic prediction method, apparatus, and computer-readable storage medium |
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Inventor after: Jiang Shengqiang Inventor after: Wan Hong Inventor after: Ye Ying Inventor after: Li Xu Inventor after: Tan Yuanqiang Inventor after: Zhang Gaofeng Inventor after: Xu Zhiqiang Inventor before: Jiang Shengqiang Inventor before: Ye Ying Inventor before: Li Xu Inventor before: Tan Yuanqiang Inventor before: Zhang Gaofeng Inventor before: Xu Zhiqiang |
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